It is often said that the $L_4$ and $L_5$ points are "60 degrees ahead and behind" a planet like Jupiter. Clearly this is true only in the case of circular orbits. In more elliptical orbits, I assume the rule of thumb would be that the $L_4$ and $L_5$ are at the points on the orbit that are equidistant from the planet and barycenter. Would that be a safe assumption?
1 Answer
From Wikipedia:
In the more general case of elliptical orbits, there are no longer stationary points in the same sense: it becomes more of a Lagrangian “area”. The Lagrangian points constructed at each point in time, as in the circular case, form stationary elliptical orbits which are similar to the orbits of the massive bodies.
A more complete answer is given in this paper. It concludes that yes, L4 and L5 are at the points on the orbit that are equidistant from the planet and barycenter.
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$\begingroup$ Interestingly, this paragraph is no longer present in the Wikipedia article on "Lagrange point" as of this date. $\endgroup$– divieiraFeb 17, 2021 at 13:22